Here is
a fantastic article about the theology that motivates ISIS:
some highlights:
Paraphrase from a related article whose link I've misplaced.
ISIS is a brand of fundamentalism that is highly Islamic: their goal is to restore Islamic rule. They are killing Muslims as well as non-believers because to them, heresy / apostasy is a more serious sin than non-belief. They believe that terrorizing non-believers is merciful because it causes them to surrender more quickly, shortening the conflict and saving lives (assuming they then convert). Other Muslims are heretics because they believe in co-existence with non-believers.
To say that ISIS is "not Islam" is like saying "fundamentalist Christians" are "not Christian." To ISIS leaders, they are the
only pure form of Islam that exists, and it is their sacred duty to impose Islamic law on the entire world.
Nothing will stop them except force. The more land they take over, the stronger they get. It is like gangrene: "oh, so what if my toe has gangrene, I don't really need my toe to walk, I'll just ignore it and hope it doesn't spread any further."
Yeah, how well does
that work?